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Full-Text Articles in Algebraic Geometry
Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg
Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms …
Application And Evaluation Of Lighthouse Technology For Precision Motion Capture, Soumitra Sitole
Application And Evaluation Of Lighthouse Technology For Precision Motion Capture, Soumitra Sitole
Masters Theses
This thesis presents the development towards a system that can capture and quantify motion for applications in biomechanical and medical fields demanding precision motion tracking using the lighthouse technology. Commercially known as SteamVR tracking, the lighthouse technology is a motion tracking system developed for virtual reality applications that makes use of patterned infrared light sources to highlight trackers (objects embedded with photodiodes) to obtain their pose or spatial position and orientation. Current motion capture systems such as the camera-based motion capture are expensive and not readily available outside of research labs. This thesis provides a case for low-cost motion capture …